A person borrowed a sum of ₹8,000 at an interest rate of 10% p.a, compounded semi-annually. What is the compound interest for a period of 1 year?

₹820

Interest is compounded half- yearly,

Rate of interest = \(\frac{10}{2}\)% = 5%

From the formula for compound interest, we know,

C.I = P(1+$\frac{R}{100})^t$– P

 = 8000 [ 1 + \(\frac{5}{100}\) ]² - 8000

 = 8000 [ \(\frac{21}{20}\) × \(\frac{21}{20}\) - 1 ]

 = 8000 [ \(\frac{441}{400}\)  - 1 ]

= 8000 [ \(\frac{41}{400}\) ]

= Rs. 820